Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is $\bm{K}$ $cm$${}^{2}$. If the prisms are glued together along a square base, the resulting prism has a surface area of $\frac{92}{47}\bm{K}$ $cm$${}^{2}$. What is the side length, in cm, of each square base?

MM

Mashaal Masha

Mar 01, 2024

Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is $\bm{K}$ $cm$${}^{2}$. If the prisms are glued together along a square base, the resulting prism has a surface area of $\frac{92}{47}\bm{K}$ $cm$${}^{2}$. What is the side length, in cm, of each square base?

Difficulty: Hard

A:

$4$

B:

$8$

C:

$9$

D:

$16$

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ID: 65e23b60e130c9f9159a169f